MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Travelling waves for chemotaxis systems

Hartmut Schwetlick


We study the existence of travelling wave solutions for Keller-Segel models, a general model of chemotaxis, where the species do not reproduce. In the case of logarithmic sensitivity we show that various functionals modelling the reactive feedback on the chemo-attractant do allow for travelling waves. In particular, a wide range of qualitatively different behaviour is possible. We can find monotone fronts as well as pulse solutions in the densities of the population and the chemical. There exists a new pattern of solutions, where both densities travel as pulses.


Related publications

2005 Repository Open Access
Hartmut R. Schwetlick

Travelling waves for chemotaxis systems